11.3 Williams College admission Data from 2013 posted on the Williams College website shows that of all 3,195 males applying, 18.2% were admitted, and of all 3,658 females applying, 16.9% were admitted. Let X denote gender of applicant and Y denote whether admitted.

a. Which conditional distributions do these percentages refer to, those of Y at given categories of X, or those of X at given categories of Y? Set up a table showing the two conditional distributions.

b. Are X and Y independent or dependent? Explain.

(Hint: These percentages refer to the population of all applicants in 2013.)

Political Party Identification Gender Democrat Independent Republican Total Female 421 398 244 1063 Male 278 367 198 843 Source: Data from CSM, UC Berkeley.

Happiness Gender Not Too Happy Pretty Happy Very Happy Total Female 154 592 336 1082 Male 123 502 257 882 Source: Data from CSM, UC Berkeley.